For the last decade there has been a generalized trend in mathematics on the search for
large algebraic structures (linear spaces, closed subspaces, or infinitely generated …

Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is
called lineable whenever A contains, except for zero, an infinite dimensional vector …

We introduce a notion of strong algebrability of subsets of linear algebras. Our main results
are the following. The set of all sequences from $ c_0 $ which are not summable with any …

We provide sharp conditions on a measure µ defined on a measurable space X
guaranteeing that the family of functions in the Lebesgue space Lp (µ, X)(p≥ 1) which are …

Dense lineability and algebrability of ℓ^{∞}∖𝑐₀ Page 1 PROCEEDINGS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 150, Number 3, March 2022, Pages 991–996 …

We show that there exist c-generated algebras (and dense in C∞([0, 1])) every nonzero
element of which is a nowhere Gevrey differentiable function. This leads to results of dense …

In this paper, sharp conditions on a measure space are provided in order that the subset of
functions in the corresponding Lebesgue space L p which are in no other L q contains …

We show that there exists an uncountably generated algebra every non-zero element of
which is an everywhere surjective function on $\mathbb {C} $, that is, a function $ f:\mathbb …

We present the method of constructing algebras and linear spaces of 2c generators using
independent Bernstein sets. As an application we obtain large algebras of special …

For a sequence $ x\in l_1\setminus c_ {00} $, one can consider the set $ E (x) $ of all
subsums of series $\sum_ {n= 1}^{\infty} x (n) $. Guthrie and Nymann proved that $ E (x) $ is …